Problem Solving PDF

Problem Solving Problem Solving I. Problem solving A. Steps involved B. Approaches: use of algorithms vs. heuristics II. Strategies for improving problem solving A. Understand the problem B. Represent problem effectively using symbols C. Means-end heuristic D. Analogy approach E. Represent informati...

Problem Solving Problem Solving I. Problem solving A. Steps involved B. Approaches: use of algorithms vs. heuristics II. Strategies for improving problem solving A. Understand the problem B. Represent problem effectively using symbols C. Means-end heuristic D. Analogy approach E. Represent information efficiently F. Promote use of parallel processing rather than serial processing G. Foster insight III. Obstacles to problem solving A. Confirmation bias B. Mental set C. Functional fixedness IV. Insight vs non-insight problems − Neural basis of insight Creativity I. Definition of creativity II. Strategies for enhancing creativity A. B. C. D. E. Increase intrinsic motivation Reduce anxiety Promote lightheartedness Incubation: take a break Brainstorming Problem Solving Studies have found that college education improves people’s problem solving/reasoning ability The ability to reason that’s developed through learning about rules of reasoning, etc. in the natural and social sciences can generalize to other domains (e.g., everyday problems) May be one reason that those with a college education have been found to handle stress better than those who have not gone to college ² Every problem contains an initial state, goal state, and obstacles ² Problem solving approaches Algorithm: a methodical, logical rule or procedure that guarantees a solution to a particular problem MAGNARA STIGNIH ALAS! NO MORE Z’S DIRTY ROOM CASH LOST IN ‘EM – One example is exhaustive search Ø Trying to solve an anagram by testing out all possible letter combinations one by one - Problem with this is that it is very time-consuming Heuristic: a rule-of-thumb strategy that allows one to reduce the number of operations that are tried in solving a problem Ø Looking only for pronounceable letter combinations (like “le” or “sa” when trying to solve an anagram) – Most everyday problems are solved using heuristics v Heuristics are speedier but also more error-prone than algorithms Strategies for Improving Problem Solving Understand the problem Ø Elevator in high rise building problem Represent the problem effectively using symbols, matrices, diagrams, and visual images Ø Buddhist Monk Problem: - At sunrise one morning, a Buddhist monk began to climb a tall mountain. He sometimes climbed the path quickly, and he sometimes went more slowly. From time to time, he stopped along the way to rest or to eat the fruit he had brought with him. Finally he reached the temple, just a few minutes before sunset. - At the temple, he meditated for several days. Then he began his descent back along the same path. He left the temple at sunrise and walked at a varying pace as before. Of course though, he walked down the hill more quickly than when he was walking up the hill. ➜ Demonstrate that there must be a spot along the path that the monk will pass on both trips at exactly the same time of day. Represent the problem in a way that is appropriate to problem solver’s background knowledge Means-end heuristic: divide problem into sub-problems and try to reduce difference between initial state and goal state for each of sub-problems Ø Hobbits-and-Orcs Problem (remember this?): - Imagine that 3 Hobbits and 3 Orcs all arrive at the right side of a riverbank, and they all want to cross to the left side. Fortunately, there is a boat. However, the boat is small, and it can hold only two creatures at one time. Moreover, whenever there are more Orcs than Hobbits on one side of the river, the Orcs will immediately attack the Hobbits and gobble them up. Therefore, you must be absolutely certain that you never leave more Orcs than Hobbits on any riverbank. How would you solve this dilemma? ➜ Sometimes it may be necessary to move backwards (hobbits-and-orcs problem) – problem-solvers are often unwilling to do this! ★ Newell and Simon developed General Problem Solver program (1957) as a way of solving complex problems using means-end analysis Ø Tower of Hanoi Analogy approach: problem solving is often a matter of finding a useful analogy between the present problem or situation and some other problem or situation with which you are more familiar Ø Candle problem: find a way to attach the candle to a wall so that it burns properly using no other objects than those on the table Ø Can find solution to candle problem through a deliberate search for a useful analogy: Shelf ➜ tack box Represent information efficiently and find shortcuts Ø Stick-configuration problem: remove exactly five sticks from the pattern so that only three squares are left, with no sticks left over ➜ Can find solution to stick-configuration problem by using a heuristic that involves thinking in terms of squares rather than sticks: “Find three squares, out of the six available, which if preserved, would allow for the removal of exactly five sticks” Promote use of parallel processing rather than serial processing – Expert anagram solvers say that solutions simply seem to “pop out” (parallel processing) – In contrast, novices generally use serial processing Foster insight: finding a solution is a matter of perceptual reorganization — any conditions that would allow your thought and perceptual processes to run more freely might help Common Obstacles to Problem Solving Confirmation bias: tendency to search for information that confirms one’s preconceptions Ø Wason card problem Statement: “If a card has vowel on one side, then it has an even number on the other side” Which card or cards below would you need to turn over in order to find out whether this rule is valid? Answer: A and 9 « Accuracy is enhanced when task describes a concrete social situation Statement: “If a person is drinking beer, they must be over 21 years of age” Each card has the drink on one side, and the person’s age on the other side: You’re the bouncer… Which of the cards below should you check out? Answer: ➜73% of students who tried drinking-age problem made correct selections, as opposed to 0% in the standard, abstract form of task In general, research has found that humans tend to be much better at reasoning with deontic conditional than they are with ordinary, nondeontic conditionals (with the Wason card problem being one example) Deontic conditionals have to do with permissions, prohibitions etc. Why are people are better at reasoning with deontic conditionals? Theory that when we solve problems with deontic conditionals, we are using a specialized module for monitoring social exchanges and detecting cheaters This is the cheater detection module (Cosmides and Tooby) Why should there be a cheater detection module? Cooperative behavior presumably has a genetic basis However, an individual who takes advantage of cooperators without reciprocating will likely do better than one who cooperates Ø Ex: They gain your trust, then steal all your bananas So how could the genes for cooperative behavior ever have become established? ➜Enter the cheater detection module… Confirmation bias and social judgments Ø Study in which participants asked to interview other student to determine if interviewee was an introvert or extravert ➜Participants who tested for extraversion tended to find interviewees extraverted and vice versa because of tendency to ask questions that confirmed trait Ø Rosenhan study v Confirmation bias may have important implication for medical diagnosis/psychotherapy - Therapist may form a less than accurate first impression of a patient and then only ask questions geared toward confirming that view ☞ Be willing to entertain the possibility that you may be wrong! Mental set: tendency to approach a problem in a particular way, especially a way that has been successful in the past but may not be helpful in solving a new problem Ø Nine dot problem: connect dots by drawing four continuous straight lines without lifting your pencil from the paper Ø Match-triangle problem: assemble six matches to form four equilateral triangles, each side of which is equal to the length of one match Ø Horse-and-rider problem: place B on A in such a way that the cowboys are correctly astride their horses à Functional fixedness: tendency to think of things only in terms of their usual functions Ø Candle problem Insight vs. Non-Insight Problems Insight: a sudden and often novel realization of the solution to a problem – Contrasts with strategy-based solutions v Insight problems are solved when answer appears suddenly v Non-insight problems are solved gradually (e.g., using means-end heuristics) Neural Basis of Insight Some critical components of insight are preferentially associated with the right cerebral hemisphere (Kounios and Beeman, 2014) At the moment when people solve problems by insight, relative to solving identical problems by analytic processing: − EEG shows a burst of highfrequency gamma-band EEG activity over the right anterior temporal lobe − fMRI shows a corresponding change in blood flow in this area Direct stimulation of right frontal-temporal cortex coupled with inhibition of left frontal- temporal cortex enhances solving of insight problems Insightful individuals show greater right hemisphere activity at rest, relative to analytic individuals Performance is enhanced or unaffected if you verbalize strategies while solving non-insight problem Performance is disrupted if you verbalize strategies while solving insight problem ☛ Differences may perhaps be explained by hemispheric specialization – left hemisphere is especially skilled at logical reasoning and language processing; the right is more spatial and holistic Priming people to think about the distant future biases them to think abstractly, causing them to perform better on insight and creativity tasks Conversely, priming people to think about the near future biases them to think concretely, causing them to perform better on analytic tasks (Förster, Jens, Friedman et al, 2004) Insightful individuals (Kounios and Beeman, 2014) Show more externally oriented attention (reduced occipital alphaband EEG activity) than do analytical individuals during the resting state Show greater internal focus of attention during the preparation phase prior to the presentation of the insight problem indicated by: − Activation of anterior cingulate (detection of weak activation of nondominant solution possibilities) − Increase in alpha-band activity over right occipital cortex ★ Probably analogous to common behavior of closing or averting one’s eyes to avoid distractions that would otherwise interfere with intense mental effort Positive mood facilitates insight, probably by increasing attentional scope to include weakly activated solution possibilities (i.e., “wide-angle vision”) ✭ Relation between broad associations/insight and positive mood is bidirectional Ø Inducing faster reading by manipulating paced reading makes participants feel more positively (Bar, M., 2009) − Reading causes the activation of concepts, and presumably, faster reading activates more concepts, which could be seen as analogous to a massive increase in broad associative activation In contrast, “rumination,” which involves dwelling on a narrow theme, is associated with depression v Similarity between insight and jokes in that both involve restructuring Creativity Creativity: finding a solution that is novel and useful To foster creativity and insight, promote conditions that allow thought and perceptual processes to run more freely Intrinsic motivation (measured by concentration on task, exploration, and enjoyment of task) promotes high levels of creativity v “The labor of love aspect is important.” – Nobel Laureate Arthur Schawlow Extrinsic motivation (being offered a reward for being creative) can reduce creativity Ø Participants who expected no particular reward for solving candle problem solved the problem more quickly than those who were told they might win a $20 reward! (Glucksberg, 1962) Conditions that increase anxiety (knowing that your work will be evaluated, having someone watch while you work, being offered a reward for being creative) tend to reduce creativity Conditions that promote lightheartedness tend to facilitate solution Ø Students who had just watched a comedy film were far more successful in solving candle problem than those who had seen either a serious film or no film (Isen, Daubman, &Nowicki, 1987) v Technique for fostering creativity: brainstorming – Brainstorming is where you get people together and just try to get ideas out, to get them up on the board – and completely suspend criticism (nothing kills creativity like the threat of criticism!) Incubation (taking a break when you get stuck on a problem) may encourage creativity – Helps you break out of mental set and see problem in new way Ø In one series of experiments, three groups of people read complex information (e.g., about apartments or European football matches) o Group 1 stated preference immediately after reading information about four possible options o Group 2, given several minutes to analyze the information, made slightly smarter decisions o Group 3, whose attention was distracted for a time, enabling their minds to engage in automatic, unconscious processing of the complex information, performed best (Strick, Dijksterhuis, & Baaren, 2010) Does a messy desk promote creativity? (Vohs, Redden & Rahinel, 2013) Ø College students were randomly assigned to spend time in adjacent office spaces − One room was exquisitely neat − The other room was wildly cluttered with papers and other work-related detritus ➜ Those in messy spaces generated ideas that were significantly more creative, according to two independent judges (Participants were also offered an apple or a chocolate bar as they exited ➜ Those who sat in the orderly office were twice as likely to choose the apple than those who sat amid the mess)